I just checked again a few minutes ago. I used my stethoscope and pinpointed the chirp to the front driveshaft. I'm almost certain that the noise is being caused by dried up needle bearings inside the double cardan joint at the rear end of it. Unfortunately that one's sealed and doesn't have a grease zerk so I'll need to have those two cross joints replaced (they're the original '92 factory units). At least it's an easy fix.